Free Internet and WIFI in Iran
Free WIFI is available in most hotels, coffee shops & restaurants in big cities like Tehran, Isfahan, Shiraz and etc.. So you can access free internet in nearly all locations in these cities, but nothing can be promised about the quality of the connection as you may face slow connection in most public places.
On the plus side a tourist sim card is easy to get by in cities as there are many official offices scattered on the map for Irancell, Hamrah-e Avval and Rightel which are the 3 main providers in Iran. also you can buy one in the airport from one of their offices. you can choose from a wide variety of Campaigns for 1$ or more. some hotels probably will charge 1$ for an hour too on their high speed service. Some guest houses provide free internet for their guests and most hotels have free WIFI in their lobbies or even rooms.
Adventure Iran can give you a sim card upon your request. This can be easier as finding the right shops to buy a sim card or dealing with locals can be hard and time consuming.
restriction and filtering is something to expect in Iran, social medias like Facebook and YouTube and twitter are filtered and some major sites are filtered too.